/// <summary>Creates a rotation matrix using the given rotation in radians.</summary> /// <param name="radians">The amount of rotation, in radians.</param> /// <returns>A rotation matrix.</returns> public static Matrix3X2 <T> CreateRotation <T>(T radians) where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T> { radians = Scalar.IEEERemainder(radians, Scalar <T> .Tau); T c, s; if (Scalar.GreaterThan(radians, Scalar.As <float, T>(-RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(RotationEpsilon))) { // Exact case for zero rotation. c = Scalar <T> .One; s = Scalar <T> .Zero; } else if (Scalar.GreaterThan(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 + RotationEpsilon))) { // Exact case for 90 degree rotation. c = Scalar <T> .Zero; s = Scalar <T> .One; } else if (!Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif + RotationEpsilon)) || Scalar.GreaterThan(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif - RotationEpsilon))) { // Exact case for 180 degree rotation. c = Scalar <T> .MinusOne; s = Scalar <T> .Zero; } else if (Scalar.GreaterThan(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 + RotationEpsilon))) { // Exact case for 270 degree rotation. c = Scalar <T> .Zero; s = Scalar <T> .MinusOne; } else { // Arbitrary rotation. c = Scalar.Cos(radians); s = Scalar.Sin(radians); } // [ c s ] // [ -s c ] // [ 0 0 ] Matrix3X2 <T> result = Matrix3X2 <T> .Identity; result.M11 = c; result.M12 = s; result.M21 = Scalar.Negate(s); result.M22 = c; return(result); }
/// <summary>Creates a rotation matrix using the given rotation in radians and a center point.</summary> /// <param name="radians">The amount of rotation, in radians.</param> /// <param name="centerPoint">The center point.</param> /// <returns>A rotation matrix.</returns> public static Matrix3X2 <T> CreateRotation <T>(T radians, Vector2D <T> centerPoint) where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T> { radians = Scalar.IEEERemainder(radians, Scalar <T> .Tau); T c, s; if (Scalar.GreaterThan(radians, Scalar.As <float, T>(-RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(RotationEpsilon))) { // Exact case for zero rotation. c = Scalar <T> .One; s = Scalar <T> .Zero; } else if (Scalar.GreaterThan(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 + RotationEpsilon))) { // Exact case for 90 degree rotation. c = Scalar <T> .Zero; s = Scalar <T> .One; } else if (!Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif + RotationEpsilon)) || Scalar.GreaterThan(radians, Scalar.As <float, T>( #if MATHF MathF.PI #else ((float)Math.PI) #endif - RotationEpsilon))) { // Exact case for 180 degree rotation. c = Scalar <T> .MinusOne; s = Scalar <T> .Zero; } else if (Scalar.GreaterThan(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(- #if MATHF MathF.PI #else ((float)Math.PI) #endif / 2 + RotationEpsilon))) { // Exact case for 270 degree rotation. c = Scalar <T> .Zero; s = Scalar <T> .MinusOne; } else { // Arbitrary rotation. c = Scalar.Cos(radians); s = Scalar.Sin(radians); } T x = Scalar.Add(Scalar.Multiply(centerPoint.X, Scalar.Subtract(Scalar <T> .One, c)), Scalar.Multiply(centerPoint.Y, s)); T y = Scalar.Subtract(Scalar.Multiply(centerPoint.Y, Scalar.Subtract(Scalar <T> .One, c)), Scalar.Multiply(centerPoint.X, s)); // [ c s ] // [ -s c ] // [ x y ] return(new( new(c, s), new(Scalar.Negate(s), c), new(x, y))); }